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Modelling of the Auditory Ribbon Synapse

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Modelling of the Auditory Ribbon Synapse Psychological and Physiological Acoustics (others): Paper ICA2016-625 Modelling of the auditory ribbon synapse Pablo Etchemendy(a), Ramiro Vergara(a) and Manuel Eguía(a) (a)Laboratorio de Acústica y Percepción Sonora, Departamento de Ciencias Sociales, Universidad Nacional de Quilmes, B1876BXD, Bernal, Bs. As., Argentina. [email protected] Abstract The coding of the fine temporal details of auditory stimuli by the auditory system is required for many auditory tasks. For instance, the temporal information conveys information necessary for the perception of pitch and for the angular localization of sound sources. The first stage where this kind of information is processed is the auditory periphery. Inside the periphery, the ribbon synapse (RS) of auditory inner hair cells excels for its temporal acuity, a fact that has driven many recent physiological and computational studies. In this work we present a biophysical model of the auditory Ribbon Synapse (RS) of inner hair cells, which contains many anatomical details obtained from the electrophysiological data available in the literature, and is able to reproduce known features of the RS, namely, temporal adaptation of exocytosis due to partial vesicular depletion and gradual increment of the exocytosis rate as the membrane is depolarized. We used the model to study some aspects that are difficult to tackle experimentally, in particular, the influence of a vesicular fusion step on: (a) the formation of a “ring-like” spatial pattern of exocitosis, compatible with the spatial structure of postsynaptic receptors; and (b) the degree of synchronization of exocytosis as a function of release event size. The results described could be relevant in order to improve our knowledge of the temporal coding of auditory stimuli at the auditory periphery level. Keywords: auditory periphery, ribbon synapse, temporal coding, computational modelling, inner hair cell Modelling of the auditory ribbon synapse 1 Introduction The auditory system excels at temporal processing tasks. Acoustic source localization, pitch perception, speech recognition and source separation, among other functions, rely on the pre- cise coding of temporal features in the range between tens of microseconds and a few mil- liseconds. In order to achieve this formidable task, the auditory system has developed several specialized mechanisms in the periphery and the first stages of neural processing. A promi- nent and widely studied structure among them is the synapse between the Inner Hair Cells (IHC) and the auditory nerve afferent fibers (spiral ganglion cells). This is the first synapse in the auditory system and is the responsible of transducing the graded potential of the IHC (in response to the basilar membrane displacements) into all-or-none events at the postsynaptic nerve fibers. This synapse bears a highly advanced and specialized structure, the synaptic ribbon, that many studies have spotted as the main responsible of completing the demanding signalling task: the sustained neurotransmitter release with high reliability, low latency and min- imum variability. This structure positions a great amount of synaptic vesicles close to release sites, within nanometers of calcium channels and directly across from postsynaptic glutamate receptors, in the so-called “active zone”. Whenever a basilar membrane displacement depolar- izes the IHC the opening probability of the calcium channels increases. It has been shown that the opening of a single calcium channel in the active zone can trigger the vesicle release (ex- ocytosis) and a postsynaptic action potential. Also, individual ribbons are capable of sustaining exocytosis at several hundreds of vesicles per second without fatigue, which is in turn reflected in rates of action potentials in individual auditory nerve fibers of hundred of hertz. Despite its phenomenal and well studied capabilities (see [1, 2] for review), a complete picture of the machinery of the ribbon synapse is still missing and many fundamental questions about its underlying mechanisms remain unanswered. For example, individual postsynaptic potentials vary in amplitude, suggesting multiquantal release of vesicles, either by homotypic fusion before exocytosis, or by synchronous exocytosis of multiple vesicles docked beneath the ribbon. Yet, a recent work has questioned the multiquantal release proposing an alternative mechanism [3]. Thus, the origin and possible roles of multivesicular release are still unclear. Also, several works have confirmed that the distribution of postsynaptic receptors displays a ring-like shape [4, 5]. Since a great part of the outstanding characteristics of the synaptic ribbon comes from its precise co-localization with presynaptic channels, it is reasonable to hypothesize that this ring-like distribution could be related to the spatial distribution of vesicle release. In this work we advance in a dynamical, yet simplified and hopefully accurate biophysical model of the auditory ribbon synapse, that could give some insight into the underlying mechanisms of this complex structure. Models are useful not only for interpreting and understanding ex- perimental results but also for testing alternative hypothesis, and for selection an planning of new experiments, as long as the models have some predictive power. Previous models of the whole ribbon synapse have been proposed either as phenomenological [6] or minimal theoreti- cal descriptions [7], and there is only one work that develops a detailed biophysical description 2 of the structure [8]. However this last model does not incorporate the multivesicular release. We will develop an experimentally constrained biophysical model focusing on the spatial and timing characteristics of the ribbon synapse and the possible roles of multivesicular release. Hence we will model in detail the spatial distribution and time events of channels and vesicles, resigning other not less important features as calcium diffusion and buffering and kinetics of calcium sensors. 2 Description of the model The main feature of the model is the description of the ribbon synapse from a spatial point of view. The synaptic ribbon is represented as a two-dimensional, square grid in which tethered vesicles are able to diffuse freely (Fig. 1). The mapping of the synaptic ribbon’s spheroidal surface to a square allows to capture one important aspect of this structure: the ribbon is believed to act as a vesicle trap, reducing the dimension of the space available for diffusion and thus helping vesicles to reach the active zone [9, 10]. Each site of the grid can be empty or filled by a single vesicle. The ribbon is divided in two regions. Sites located at three sites or less from the center define the active zone (AZ), which corresponds to the lower region of the ribbon. Vesicles located at the active zone are in contact with the plasmalemma, and near to voltage-gated CaV1.3 calcium channels located within the plasma membrane [11]. In hair cells, these channels are colocalized with the synaptic body [12], which facilitates the interaction between the entering Ca2+ and the neighboring vesicles exocytic sensors. In the model, a total of 80 calcium channels [13] are located within a 4.5-sites radius from the AZ center. The middle and upper regions of the ribbon are represented by the remaining sites. Vesicles can enter the ribbon through a simple refilling process, controlled by the probability per free site and per time unit that a free vesicle gets tethered to the ribbon. Only sites outside the active zone can accept new vesicles and the process is unidirectional; vesicles can abandon the ribbon only through exocytosis. The combination of refilling, diffusion and exocytosis processes allows to model the continuous activity of the auditory synaptic ribbon, and therefore investigate aspects related to the reliable transmission of long-lasting auditory stimuli. In the rest of this section we will describe the details of the model and its implementation. In Table 1 we list the model parameters along with the references from the literature used to set their values. The model was implemented in Matlab 2013. Calcium channels dynamic was solved using Gillespie’s “direct method” [14], with an upper limit for the sampled time to next reaction set to 0.01 ms for variable inputs. 2.1 Anatomic aspects The grid has a size of 13×13 sites, thus having a total of 169 sites. The active zone (AZ) is defined by a circle of radius RAZ equal to 3 sites, which gives a total of 29 sites. These figures are between the values reviewed by Nouvian et al. [15] for the ribbon-associated vesicles at the mouse IHC (125 to 200 vesicles, depending on the microscopy method) and for the docked vesicles at the AZ (16 to 30 vesicles). Each site can be considered as having a size of 40×40 3 Figure 1: (a) Schematic of the anatomy of the synapse. The elements included in the model are the synaptic ribbon, the synaptic vesicles and the calcium channels located at the cellular membrane. (b) Spatial grid describing the synapse. The legend on the right shows the correspondence between anatomy and model. nm, thus representing a 20-nm radius vesicle [16]. The total number of calcium channels (NCC) is the mean number of ribbon-associated calcium channels considering all synapses in the entire cell [13]. We assumed a uniform distribution of channels inside a circle of radius RCC located at the base of the synaptic body, concentric with the active zone; in each simulation channel locations were sampled at time zero and then remained constant. RCC was set to 4.5 sites, a value a little greater than RAZ, which guarantees that inner and outer sites of the active zone are surrounded by the same number of channels in average. 2.2 Dynamic of calcium channels and exocytosis mechanism Each calcium channel is stochastically modelled by a simple two-state scheme: a O )−−−−* C (1) b where O represents the “open” state and C the “closed” state. Transitions between states are governed by the voltage-dependent rates a(V) (opening) and b(V) (closing): h h −1 a(V) = a0 · (V −Va ) · (1 − exp((Va −V)=ka )) ; h −1 (2) b(V) = b0 − b1 · (1 + exp((V −Vb )=kb )) ; Parameter values were obtained by fitting the experimental data referred by Wittig and Parsons [8].
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